You won't need Decimal to replace Java's BigInteger of course, as Python's
integers are already big.
Here I just redid your Mersenne Primes exercise using native Python ints,
and also exposing the guts of a probable prime test that seems less flaky
than the one you had to use (set at 50% reliable -- and changing its mind a
lot, as there's randomness involved).
The test I use is the Miller-Rabin test, with a citation to a certain page
number in Knuth.
Here's the output:
runfile('/Users/mac/Documents/School_of_Tomorrow/mersennes.py',
wdir='/Users/mac/Documents/School_of_Tomorrow')
M1 = 2**2-1 = 3
M2 = 2**3-1 = 7
M3 = 2**5-1 = 31
M4 = 2**7-1 = 127
M5 = 2**13-1 = 8191
M6 = 2**17-1 = 131071
M7 = 2**19-1 = 524287
M8 = 2**31-1 = 2147483647
M9 = 2**61-1 = 2305843009213693951
M10 = 2**89-1 = 618970019642690137449562111
M11 = 2**107-1 = 162259276829213363391578010288127
M12 = 2**127-1 = 170141183460469231731687303715884105727
M13 = 2**521-1 =
6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151
M14 = 2**607-1 =
531137992816767098689588206552468627329593117727031923199444138200403559860852242739162502265229285668889329486246501015346579337652707239409519978766587351943831270835393219031728127
Here's the source code (which thanks calcpage and links to your video in
the opening docstring):
https://github.com/4dsolutions/School_of_Tomorrow/blob/master/mersennes.py
As you'll see from lines 127 on, I do a brute force trial by division at
first, to determine primehood, then switch to this more exotic algorithm
going forward. It gets them all right.
Once students develop an appetite for big integers, they're going to wonder
about big reals (so called arbitrary precision). We can switch them to a
full-blown math framework like Sage, but we don't have to, given these
smaller libraries (decimal, gmpy2) are close at hand.
Kirby
On Sun, Feb 2, 2020 at 5:36 PM A. Jorge Garcia <calcp...@aol.com> wrote:
> And here's BigInteger at work finding large Mersene Primes.
> https://youtu.be/-Snd7a55FrE
>
> I'm gonna have to do the same in python with Decimal. What about the N()
> method in SAGE and numpy?
>
> Regards,
> Al
>
> Sent from BlueMail <http://www.bluemail.me/r?b=15774>
> On Feb 2, 2020, at 19:18, kirby urner <kirby.ur...@gmail.com> wrote:
>>
>> Hi Jorge --
>>
>> I agree, it'd be interesting to apply a Riemann Sum algorithm using
>> arbitrary precision as the number crunching type, versus IEEE754.
>>
>> Freed from FORTRAN, you would have that option. I'll do it now...
>>
>> [ sometime later ]
>>
>> Here's a sandbox version:
>> https://repl.it/@kurner/computepi
>>
>> I'm comparing the convergent Rsum you give with one of Ramanujan's:
>>
>> pi = 3.141591653589626571795976716612836217532486859692
>> start_time = 23183.62579051
>> end_time = 23205.729972367
>> elapsed time = 22.104181857001095 seconds
>>
>> Ramanujan's converges really quickly, after 100 terms:
>>
>> pi = 3.141592653589793238462643383279502884197169399375
>> start_time = 23205.731066136
>> end_time = 23205.838047055
>> elapsed time = 0.10698091900121653 seconds
>>
>> That 2nd answer is correct as far as I'm showing it. One may tweak the
>> repl to get even more precision.
>>
>> I wonder how fast REPL.it is compared to my R-Pi. I'll be checking that
>> later.
>>
>> You're getting into clustering, cool!
>>
>> That's a deep topic, with or without converging to Pi, wish I knew more.
>>
>> Kirby
>>
>> On Fri, Jan 31, 2020 at 8:30 PM < calcp...@aol.com> wrote:
>>
>>> Hi Kirby,
>>>
>>> Love your post about arbitrary precision. I wish I had seen it before I
>>> started a project with my students computing PI on a Linux Cluster.
>>> Here's my blog post about our project so far if anyone is interested,
>>>
>>> https://shadowfaxrant.blogspot.com/2019/12/cistheta-2019-2020-meeting-7-121519.html
>>>
>>> Regards,
>>> A. Jorge Garcia
>>> Teacher and Professor
>>> Applied Math, Physics and Computer Science
>>> http://shadowfaxrant.blogspot.com
>>> http://www.youtube.com/calcpage2009
>>>
>>>
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